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Q.
The area bounded by $y -1=| x |, y =0$ and $| x |=\frac{1}{2}$ will be :
Application of Integrals
Solution:
The given lines are, $y -1= x , x \geq 0 ; \quad y -1=- x , x <0$
$y =0 ; \,\,\,\,x =-\frac{1}{2}, x <0 ; \,\,\,\, x =\frac{1}{2}, x \geq 0$
so that the area bounded is as shown in the figure.
Required area $=2 \int\limits_{0}^{1 / 2}(1+ x ) dx =2\left(x+\frac{x^{2}}{2}\right)_{0}^{1 / 2}=\frac{5}{4}$
